Abstract
We propose a new mathematical model to learn capillary leakage coefficients from dynamic susceptibility contrast MRI data. To this end, we derive an embedded mixed-dimension flow and transport model for brain tissue perfusion on a subvoxel scale. This model is used to obtain the contrast agent concentration distribution in a single MRI voxel during a perfusion MRI sequence. We further present a magnetic resonance signal model for the considered sequence including a model for local susceptibility effects. This allows modeling MR signal-time curves that can be compared with clinical MRI data. The proposed model can be used as a forward model in the inverse modeling problem of inferring model parameters such as the diffusive capillary wall conductivity. Acute multiple sclerosis lesions are associated with a breach in the integrity of the blood-brain barrier. Applying the model to perfusion MR data of a patient with acute multiple sclerosis lesions, we conclude that diffusive capillary wall conductivity is a good indicator for characterizing activity of lesions, even if other patient-specific model parameters are not well-known.
Highlights
Multiple sclerosis (MS) is characterized by a cascade of inflammatory reactions that result in the formation of acute demyelinating lesions (MS plaques)
We propose that the local distribution of the contrast agent and resulting local susceptibility effects obtained by a sub-voxel scale model may better explain the nuclear magnetic resonance (NMR) signal response of the tissue
We presented a mixed-dimension fluid-mechanical model for contrast agent brain tissue perfusion on the sub-voxel scale
Summary
Multiple sclerosis (MS) is characterized by a cascade of inflammatory reactions that result in the formation of acute demyelinating lesions (MS plaques). Mathematical models (forward model) for contrast agent perfusion in the brain tissue can help understanding the underlying reasons for a particular intensity–time curve of a voxel, by identifying and analyzing the model parameters which are able to reproduce the MRI data. This process is known as solving the inverse problem. We propose that the local distribution of the contrast agent and resulting local susceptibility effects obtained by a sub-voxel scale model may better explain the NMR signal response of the tissue The application of this new perfusion model is demonstrated for the example of MS lesions. We call the scale below the meso-scale, which includes the molecular scale, micro-scale, and refer to the scale above as macro-scale
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